-
[1]
| 引用本文: |
|
| Citation: |
|
计量
- 文章访问数: 4032
- PDF下载量: 560
- 被引次数: 0
物理学报. 1957, 34(1): 58-68.
doi: 10.7498/aps.13.58.
从截面上晶粒大小的面密度分布计算体密度分布
- 收稿日期: 1956-08-18
- 刊出日期: 1957-01-20
摘要: 在截面上可以测定晶粒依直径大小分布的面密度。利用夏耳和萨尔忒可夫方法可以将面密度换算到体密度。这些方法主要是解多元联立一次方程。本文提出一个新的方法;直接解积分方程,利用拉普拉斯变换求出体密度的解。将所得结果和以前的结果对照,发现有一些差异;即过去的计算的结果一般使密度偏低,并且在变化较大的区间无法正确地估计及计算出来。本文的方法是严格的,可以知道各处的精确程度。在一个具体的例中来表示出这一点。
English Abstract
AN ANALYTICAL METHOD OF SOLUTION OF THE DISTRIBUTION FUNCTION OF CRYSTAL SIZES IN A VOLUME
- Received Date:
18 August 1956
- Published Online:
20 January 1957
Abstract: The distribution function of crystal sizes on a cross-sectional surface can be obtained by direct observation. By using the well-known Scheil-салIтъIков method one can deduce the volume distribution function. Their method consists chiefly in solving a system of simultaneous linear algebraic equations, in which certain approximations are adopted without explicit criterions. The present paper proposes an analytical method of solution, in which operational calculus and Laplace transform are applied. The density function thus obtained is somewhat in variance with those of Scheil and others; namely, values obtained by the previous authors appear a little lowered as compared with ours. As the present method is rigourous and the numerical computations so far performed are within criterious in accuracy, the difference may well be attributed to the errors introduced by the approximations in the old methods. This fact is fully demonstrated by a concrete example in the text.
下载: